(A) modified approximation algorithm for criticality index in stochastic PERT networks

Abstract

The main topic of this thesis is the criticality of activities regarding stochastic PERT networks. PERT network model has been widely and successfully used in many real world decision making environments. But theoretical improvements to extend the traditional PERT decision model has been limited. Considering this fact we concentrate on the key concept of the PERT model. When we consider the PERT model as a decision making tool for allocation of scarce resources to activities it is necessary to have a basis of the decision. Traditional PERT model uses the concept of slack for each activity. the concept of slack is generalized to criticality in stochastic PERT networks. Therefore when there are much uncertainties in the activity times the criticality plays the central role in the decision making. In spite of the importance of the criticality there has not been appropriate methods obtain the value of the criticality. Recently an approximation algorithm that can be applied in practical situations has been developed. In this thesis we modify this algorithm so that computational requirements and computer memory usage are diminished. Computational test shows that the modified algorithm performs well in most cases. Practical guide is presented about the time when the modified algorithm is appropriate.